2018-09-04 | Course overview |
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2018-09-06 | Electrical networks, harmonic functions, existence and uniqueness for Dirichelet problems, voltage as hitting probabilities. Following Lyons-Peres. |
2018-09-11 | Effective conductance and resistence, equivalence to recurrence and transience. Star and cycle spaces. |
2018-09-13 | Rayleigh Monotonicity Principle, random paths, Nash-Williams bound, Recurrence and transience of Z^d, resistance and return probabilities in Z^2. |
Assignment 1 | Due 2018-09-25. problems, LaTeX |
Assignment 2 | Due 2018-10-19. problems, LaTeX |
2018-10-30 | Ising model: Gibbs measures, existence of limits and phase transitions. |
2018-11-01 | Phase transition for mixing of the Ising model: Curie Weiss model and the lattice. Spectral methods for reversible Markov chains. |
Assignment 3 | Due 2018-11-15. problems, LaTeX |
2018-11-08 | Percolation: definitions, critical probability, transition in Z^d. |
2018-11-13 | Percolation: Harris-FKG inequality, 0-1-infinity rule for transitive graphs, uniqueness in amenable graphs. No percolation in Z^2 at p=1/2. |
2018-11-13 | Percolation: Russo's formula, Russo-Seymour-Welsh, Sharpness of the phase transition (Duminil-Copin + Tassion) |
Assignment 4 | Due 2018-11-29. problems, LaTeX |